Planetary Signatures in the SAO 206462 (HD 135344B) Disk: A Spiral Arm Passing Through Vortex?

1.3 MB·

by  Jaehan Bae

Draftversion February23,2016
PreprinttypesetusingLATEXstyleemulateapjv.5/2/11
PLANETARY SIGNATURES IN THE SAO 206462 (HD 135344B)DISK: A SPIRAL ARM PASSING THROUGH
VORTEX?
Jaehan Bae1, Zhaohuan Zhu2,3, Lee Hartmann1
Draft versionFebruary 23, 2016
ABSTRACT
6 The disk surrounding SAO 206462, an 8 Myr-old Herbig Ae star, has recently been reported to
1 exhibit spiral arms, an asymmetric dust continuum, and a dust-depleted inner cavity. By carrying
0 out two-dimensional, two-fluid hydrodynamic calculations, we find that a planetary-mass companion
2 locatedatthe outer disk couldbe responsible for these observedstructures. Inthis model, the planet
excites primary and secondary arms interior to its orbit. It also carves a gap and generates a local
b
pressurebumpattheinnergapedgewhereavortexformsthroughRossbywaveinstability. Thevortex
e
F traps radially drifting dust particles, forming a dust-depleted cavity in the inner disk. We propose
that the vortex is responsible for the brightest southwesternpeak seen in infrared scattered light and
2 sub-millimeterdustcontinuumemission. Inparticular,itispossiblethatthescatteredlightisboosted
2
as one of the spiral arms passes through the high density vortex region, although the vortex alone

] may be able to explain the peak. We suggest that a planetary companion with a mass of 10–15 MJ
P is orbiting SAO 206462 at 100–120au. Monitoring of the brightest peak over the next few years will
E help reveal its origin because the spiral arms and vortex will show distinguishable displacement.
Subject headings: planet-disk interactions — protoplanetary disks — stars: individual (SAO 206462)
.
h
p
- 1. INTRODUCTION cavity.
o
The scattering of optical and near-infrared light and
r The protoplanetarydisk aroundSAO 206462is one of
t the thermal sub-millimeter emission reflect not only the
s the few systems so far to exhibit asymmetric features
gasstructurebutthespatialdistributionofthedustpar-
a in both near-infrared scattered light and sub-millimeter
[ thermal emission. Direct polarimetric imaging revealed ticles with different sizes. The small dust responsible
for the scatteredlight should be well-coupled to the gas,
twospiralarmsintheHandK bands(Muto et al.2012;
2 s but larger grains responsible for millimeter-wave emis-
Garufi et al. 2013), and the dust continuum emission at
v sion can be concentrated by pressure gradients.
sub-millimeterwavelengthsobservedwithALMAshowed
6
In this work, we test whether a planetary-mass com-
7 avortex-likefeatureaswellasadust-depletedinnercav-
panionis able to generatevarious structures observedin
9 ity (P´erez et al. 2014; van der Marel et al. 2015, 2016).
theSAO206462disk. Inordertotestourmodelsagainst
4 Onepossiblyinterestingfeatureisthatthescatteredlight
near infrared scattered light and sub-millimeter thermal
0 observationsindicateanabruptchangeinbrightnessand
emission,weperformtwo-fluidcalculationswherewecan
. pitch angle in one of the arms, while most models show
1 simulatedustaswellasgasstructures. Basedonthecal-
smooth spiral structure (e.g. Fung & Dong 2015).
0 culations, we show that the observed structures are well
Recent studies have shown that planet-driven spiral
6 reproducedwitha10–15M planetorbitingSAO206462
arms may explain the observed scattered light in near- J
1 at 100–120 au. The abrupt change in brightness in one
infrared (e.g. Dong et al. 2015; Zhu et al. 2015). Upon
:
v their formation, planets excite density waves in disks ofthearmscouldbeproducedasthearmpassesthrough
i with different azimuthal modes. While the different the high density vortexregion,though vortexalone may
X be able to explain the bright scattered light peak. We
modes tend to interfere with each other and merge
r discuss possible future observations that will help reveal
to a single spiral arm (Ogilvie & Lubow 1999), it is
a the originofthe structuresseeninSAO 206462disk and
found that a secondary can also exist and the separa-
better constrain planetary mass and position.
tion between these two arms increases with the planet
mass (e.g. Fung & Dong 2015; Zhu et al. 2015). Plan-
2. NUMERICAL METHODS
ets are also capable of generating vortices at the in-
ner and outer gap edge, where pressure has local max- 2.1. Disk Model
ima(Koller et al.2003;Li et al.2005;de Val-Borro et al.
We begin with an initial power-law surface density of
2007;Lin & Papaloizou2010;Lyra & Lin2013;Fu et al.
the disk gas
2014a,b; Zhu & Stone 2014; Zhu et al. 2014). The vor- R −1
tices efficiently trap dust particles and impede dust mi- Σ (R)=Σ , (1)
g p
grating inward, possibly forming a dust-depleted inner (cid:18)Rp(cid:19)
where Σ is the gas surface density and Σ is the gas
g p
[email protected], [email protected], [email protected] surface density at the semi-major axis of the planetary
1Department of Astronomy, University of Michigan, 1085 S. orbit R . The power-law density slope of −1 is con-
UniversityAvenue,AnnArbor,MI48109, USA p
2DepartmentofAstrophysicalSciences,PrincetonUniversity, sistent with the best solution of Carmona et al. (2014,
4IvyLane,PeytonHall,Princeton,NJ08544, USA see their model 5) found in between 30 and 200 au. We
3HubbleFellow. chooseΣpsuchthattheinitialtotalgasmassis0.026M⊙
2 Bae et al.
TABLE 1
ModelParameters
Parameter Value
Stellarmass(M∗) 1.7M⊙a
Diskmass(Mdisk) 0.026M⊙b
Diskaspectratioatplanet’sorbit((H/R)p) 0.1
Planetmass(Mp) 5,7.5,10,12.5,15,17.5,20MJ
Semimajoraxisoftheplanet(Rp) 80,90,100,110,120,130,140au
Minimumgrainsize(amin) 0.1µm
Maximumgrainsize(amax) 5.3mm
a
Mu¨lleretal.(2011)
b
Andrewsetal.(2011)
(Andrews et al. 2011). comparable radial and azimuthal sizes at all radii.
In these two-dimensional (R,φ) simulations, we use a
fixedradialtemperaturedistributionwiththeisothermal 2.2. Dust Component
equation of state, which implies that the ratio of disk
Thedustresponsetoplanet-generatedgasstructuresis
scale height to radius is
calculatedwiththetwo-fluidFARGOcodeintroducedin
H H R 0.25 Zhu et al.(2012), in which the dust component is added
= , (2) to the standard FARGO code (Masset 2000). To briefly
R (cid:18)R(cid:19)p(cid:18)Rp(cid:19) summarize,we solve an additional mass and momentum
equation set for the dust component. We treat the dust
where (H/R)p is the aspect ratio at planet’s semi-major component as an inviscid, pressureless fluid so dust sim-
axis. We use (H/R)p = 0.1 which results in the corre- ply feels the drag force in addition to the central stellar
sponding disk temperature profile potential. The drag terms are added to the momentum
equation as an additional source step
R −0.5 R −1
p
T =44 K (3) ∂v v −v
(cid:18)Rp(cid:19) (cid:18)100 au(cid:19) R,d =− R,d R,g (4)
∂t t
s
with M∗ = 1.7M⊙ and mean molecular weight of 2.4. and
The temperature profile is roughly consistent with de-
∂v v −v
φ,d φ,d φ,g
tailedflareddiskmodels,includinggoodagreementwith =− , (5)
∂t t
estimates of the disk scale heights for SAO 206462 from s
Andrews et al. (2011) and Carmona et al. (2014). Also, wherev andv areradialandazimuthalvelocities,and
R φ
the temperaturedependence onradiusis consistentwith the subscripts g and d denote gas and dust components.
the assumption of a constant α and Σ ∝ R−1 (for a The dust stopping time is t = πρ a/2Σ Ω with ρ and
s p g p
steady disk). a being dust particle density and size.
For the gas component a uniform viscosity parameter Sincedustparticlescandiffuse inthe gaseousdiskdue
α=10−4 is implemented. Vortex formationthroughthe toturbulence,dustdiffusionisimplementedintheopera-
Rossby wave instability (RWI) could be dependent on torsplitfashioninthesourcestepofthedustcomponent
the choice of α value as seen in numerical simulations (Clarke & Pringle 1988):
(e.g. Bae et al. 2015). Empirically, it has been shown
that the width of the gas pressure maximum has to be ∂Σd Σd
=∇· DΣ ∇ . (6)
.2H in order for the RWI to develop (Lyra et al. 2009; ∂t (cid:18) g (cid:18)Σ (cid:19)(cid:19)
g
Reg´aly et al. 2012). Although determining the critical
upper α value for which our results remain valid could In the above equation, D = ν/Sc is the turbulent diffu-
bedoneonlynumericallygiventhecomplexityofthedisk sivity where ν is the gas viscosity and Sc=1+(Ωts)2 is
structure (planet, spiral arms, vortex, their interaction, the Schmidt number (Youdin & Lithwick 2007).
etc.), adopting this criterion, one could make a simple We perform calculations with five different dust sizes:
argument that the viscous timescale at the inner gap 30,100,300,1000,3000µm,whichrepresentparticlesin
edge (t ; the timescale that the disk viscously spreads size bins of [17 µm, 53 µm], [53 µm, 170 µm], [170 µm,
ν
out the gas pressure bump by ∼ H) has to be longer 530 µm], [530 µm, 1700 µm], [1700 µm, 5300 µm], re-
than the vortex formation timescale. In an alpha disk, spectively. We assume that the dust particles have a
the corresponding viscous timescale can be written as power-law size distribution dn(a) ∝ a−3.5da in between
tν =H2/ν =P/(2πα), where ν =αH2Ω is the viscosity amin = 0.1 µm and amax = 5.3 mm. We note that
and P = 2π/Ω is the local orbital period. We find that we do not perform calculations for the particles with
vortices form at the inner gap edge within 10–20 local a< 17 µm, and simply assume that those particles per-
orbital time; thus, unless the viscosity parameter is as fectly follow the gas distribution when producing syn-
large as ∼0.01 our results should remain valid. thetic ALMA observations in Section 4. The dust mass
Weadoptinnerandouterboundariesat20and300au. in each size bin is determined based on the particle size
We use 288 logarithmically spaced radial grid-cells and distribution of dn(a)∝a−3.5da, which provides the sur-
688 linearly spaced azimuthal grid-cells, with which face density as a function of a: dΣ (a) ∝ a−0.5da. The
d
choice ∆R/R is constant to 0.009 and grid-cells have massfractionsineachsizebinof[0.1µm,17µm],[17µm,
PLANETARY SIGNATURES IN SAO 206462 3
Fig. 1.—Distributionsof(left)gas,(middle)30µmdust,and(right)300µmdustatt=50Tp inφ−Rcoordinates. Mp=10MJ and
Rp =100 AU wereused. Theplanet excites primaryand secondary armsatthe inner disk. Italsogenerates horseshoe regionand opens
agap. Two vortices areformedat the inner and the outer gap edge. The imageis shifted inazimuth fromits originalina way that the
planetlocates atφ=180◦.
53 µm], [53 µm, 170 µm], [170 µm, 530 µm], [530 µm,
1700 µm], [1700 µm, 5300 µm], are 5.3 %, 4.4 %, 7.9 %,
13.8 %, 25.1 %, 43.6 %, respectively. The total initial
dust surface density is assumed to be 1 % of the gas
density. We assume that the dust density is 3 g cm−3.
We vary the planet’s mass and semi-major axis to
model the SAO 206462 disk. The model parameters are
summarized in Table 1.
3. RESULTS
Allthecalculationswererunfor100T whereT refers
p p
tothe orbitaltime atthe planet’s location. We findthat
the spiral structure is well developed within 2 T and
p
remains steady afterward. The planet carves a gap and
generates a horseshoe orbit region around its orbit. It
also generates vortices at the inner and outer gap edges.
Thevortexattheinnergapedgeformswithin∼5T and
p
survives until the end of the calculations. The duration
of the calculationsis thus long enoughfor the structures
to fully develop in the disk.
Figure 1 shows gas, 30 µm dust, and 300 µm dust
distributions at 50 T with a 10 M planet orbiting at
p J
100 au. The horseshoe region, primary and secondary
inner spiral arms, and an azimuthally elongated vor-
tex can be clearly seen. Dust depletion takes place in
the inner disk (∼40–50 au for a = 30 µm, ∼30–50 au
for a = 300 µm) and it is more significant for larger Fig.2.— Distribution of the Stokes number Ts corresponding
tothegas distributionshowninFigure1. Notethat thenumbers
dust particles because they suffer strongerdrag. The in-
giveninthecolorbararefortheparticleswitha=30µm.
ner dust cavity grows over time, and at the end of the
calculation (t = 100 T ) particles with a ≥ 1 mm are
p
completely cleared from the inner disk. The outer vor- responsible for the sub-millimeter thermal emission.
tex is prominent in our simulations, but not seen in the The width of the horseshoe region (xhs) is about
ALMAsub-millimeterthermalemissionmappresumably 25 au, which is in good agreement with a known re-
because the actual SAO 206462disk has a faster decline lation between the local disk aspect ratio h = H/R
insurfacedensity withradiusthaninourmodelatlarge and the planet-to-star mass ratio q = Mp/M∗: xhs ∼
radii (& 100 au; Andrews et al. 2011): our model disk R q/h (Masset et al. 2006; Baruteau & Masset 2008;
p
has more mass in the outer disk than the observational Paaprdekooper& Papaloizou2008).
estimates for the actual disk. It is also possible that a The vortexefficiently trapsdust particles,particularly
slowdustgrowthrateatlargeradiilimitsdustmasswith the ones with a stopping time of the order of the lo-
a & 100 µm in the outer disk of SAO 206462, which is cal orbital time as expected in typical anticyclonic vor-
4 Bae et al.
Fig. 3.— (Left) Polarized scattered light observed in the Ks band by Garufietal. (2013). The brightness is scaled with R2 to com-
pensate for stellar light dilution, and is in the arbitrary linear scale. We used publicly available data from the Vizier online catalog
(http://vizier.cfa.harvard.edu/viz-bin/VizieR?-source=J/A+A/560/A105). (Middle) Same as the left panel but in φ−R coordinates
where φ is defined as the angle measured counter-clockwise from the north. (Right) Dust continuum emission obtained with ALMA at
690 GHz by P´erezetal. (2014). We used publicly available data from the ALMA archive. In the left and middle panels, we label some
important structures: S2refers tothe arm onthe eastern side, S1refersto the armthat extends fromthe north to west, and V refersto
thebrightestpeakonthesouthwesternside.
tices(e.g.Barge & Sommeria1995;Inaba & Barge2006; also shows a bright azimuthal feature (hereafter V) at
Meheut et al. 2012; Fu et al. 2014b; Zhu & Stone 2014; (∆R.A.,∆decl.) = (−0.25′′,−0.3′′). Interestingly, the
Bae et al. 2015). As a result the dust-to-gas mass ra- bright feature in S1 in the scattered light is spatially
tio inside the vortex becomes as large as ∼ 1 : 25. coincident to the southwestern dust emission peak.
In Figure 2 we present the distribution of the Stokes When the scattered light is plotted in φ − R coor-
number T that corresponds to the model presented in dinates, however, the pitch angle of the western arm
s
Figure 1. The Stokes number in the vortex is about changes abruptly in between S1 and V. This raised the
10−3–10−2 for the 30 µm particles and is close to unity followingquestion: doS1 andVformasingle spiralarm
for millimeter-sized particles. As the Stokes number in- and share a common physical origin? Or do they have
creasesagainstthe particlesize(T ∝a), largerparticles different physical origins, but are just spatially coinci-
s
exhibit a more compact structure. For the 300 µm-sized dent?
dust, the vortex extends ∼ 180◦ in azimuth. The total Inordertoinfertheoriginofthestructuresandtoesti-
(gas+dust)massintheinnervortexvariesovertime,but matetheplanet’smassandlocation,wecomparethesim-
it is about 3 M at 50 T , which is roughly consistent ulated surface density distribution and synthetic ALMA
J p
to the mass constrained by sub-millimeter observation observationstotheobserveddata. Wenotethatcompar-
(2 M ; P´erez et al. 2014). ison between the simulated surface density distribution
J
Regarding the inner arms, we find that the secondary andthescatteredlightimageshouldbetreatedwithcau-
arm becomes significantly fainter outside of ∼ 60 au, tion for several reasons.
whereas the primary arm extends further out to the The near-infrared scattered light only traces the fluc-
planet. The faint secondary arm at & 60 au may be tuations of the disk atmosphere since the disk is highly
due to the fact that less material exists because of the optically thick at these wavelengths. Furthermore, the
gap opened by the planet. However, this may also be spiral shocks complicate the three-dimensional struc-
because the second spiral arm is excited at m=2 Lind- ture (Zhu et al. 2015). Therefore, it is not straight-
blad resonance, which resides at R ∼ 0.63 R . We note forward to directly relate the disk surface density to
p
that the pitch angle of the primary arm increases as a the scattered light images. However, the shape of the
function of radius, especially near the planet, while that spiral arms are similar at different heights in the disk
of the secondary arm is nearly constant over radius. It (Figure 2 of Zhu et al. 2015) and similar to the spiral
is also worth pointing out that the vortex and the inner shape in the modeled scattered light images (Figure 2
spiralarmsrotateatdifferentfrequencies: the vortexor- of Fung & Dong 2015). Thus, we compare the morphol-
bitsatthelocalKeplerianspeedwhereasthespiralarms ogy of the arms and density distribution in a qualitative
corotate with the planet. manner, rather than in a quantitative manner.
The synthetic ALMA observations are produced as
4. DISCUSSION follows. We use the Mie theory to calculate the dust
opacity at 690 GHz. For particle sizes of 30, 100, 300,
InFigure3,wedisplaythescatteredlightimageatthe
1000, 3000 µm, the dust opacities are 12.0, 12.9, 7.6,
K band (Garufi et al. 2013), and the dust continuum
s 2.3, 0.6 cm2g−1, respectively. For particles smaller than
emission at 690 GHz (P´erez et al. 2014). In the scat-
17 µm, we use the opacity at a = 3µm as a represen-
tered light image, the disk shows two well-established
tative value (2.4 cm2g−1). We note that the resulting
spiral arms; one on the western side (hereafter S1)
synthesized images are not sensitive to the choice of the
and the other on the eastern side (hereafter S2). It
PLANETARY SIGNATURES IN SAO 206462 5
Fig.4.— Upper panels: when S1 is assumed to be the primary arm. Mp = 10 MJ and Rp = 100 au were used. (Left) Gas density
distributionintheinner140 audisk(=1′′)fromthiswork. Theplanetislocated at(∆R.A.,∆decl.)=(0.′′3,−0.′′65). (Middle)Sameas
the left panel, but in φ−R coordinates where φ is measured counter-clockwise from the north. The primaryand secondary inner spiral
arms as well as the vortex are clearly seen. (Right) ALMA simulated image with the cycle 0 extended configuration. The synthesized
beam is displayed in the lower-leftcorner. Lower panels: same as the upper panels, but when S2 is the primaryarm. Mp =15 MJ and
Rp=120auwereused. Theplanetislocatedat(∆R.A.,∆decl.)=(−0.′′4,0.′′75)intheleftpanel.
opacityofa<17µmparticlesbecausethemassfraction using CASA4. Thermal noise from the atmosphere and
for the particles are only 5.3 % (see Section 2.2). Then, from the ALMA receivers is added by setting the ther-
we calculate the optical depth of the disk as malnoise option in the simobserve task to tsys-atm. We
usetheALMAcycle0extendedconfigurationtocompare
our models to the data presented in P´erez et al. (2014,
τ =S W Σ κ , (7)
i d,i i see also Figure 2 of this paper). The distance of 140 pc
Xi (Mu¨ller et al. 2011, and references therein), PA and in-
clinationof63◦ and16◦ (van der Marel et al.2016)were
whereWi isthemassfraction(0≤Wi ≤1, Wi =1)of used.
each dust size bin, and Σd,i and κi are thePdust surface For the entire duration of our simulations (100 Tp .
density and the opacity for each dust size bin, respec- 105 year)µm-sized dust particles are not completely de-
tively. ThescalingfactorS isintroducedtocalibratethe
pletedfromtheinnerdisk,whilesub-millimeterandmil-
overalldust-to-gasratioinawaythatthesimulatedther-
limeter continuum observations suggest a significant re-
mal emission matches to the observed intensity. In the
duction of dust density in the inner cavity (Lyo 2011;
models introduced below, we use S ∼ 2, which implies
van der Marel et al. 2015, 2016). This is probably be-
that the dust-to-gas mass ratio is presumably smaller
cause the duration of the simulations is much shorter
than the one assumed in our calculations (1:100). The
than the actual age of the system, although we cannot
totalfluxdistributioniscalculatedwiththetemperature
rule out the existence of a second companion inside the
profile given in Equation (3), assuming the blackbody
cavity. In order to reduce the excess dust emission from
radiation with the effect of optical depth taken into ac-
the inner disk, we decrease the dust density at the in-
count: F = B (T)exp(1−τ), where F is the flux, B
ν ν
denotes the Planck function, and τ is the optical depth.
Finally, the flux is synthesized with the ALMA beam 4 http://casa.nrao.edu
6 Bae et al.
Fig.5.— Distributionof optical depth at 690 GHz for the two models presented inFigure 4. We note that the entire disk is optically
thinatthisfrequency,andonlythecoreofthevortexismarginallyopticallythick.
ner 35 au by a factor of 100 when we produce synthetic arms in this scenario is still a question.
ALMA observations. When S2 is assumed to be the primary arm, V and
Zhu et al. (2015) and Fung & Dong (2015) recently S1 in the scattered light probably have a different origin
showed that the azimuthal separation of scattered light becauseitisunlikelythat(1)thesecondaryarmextends
from the primary and secondary arms is a function of further out than the primary and (2) the pitch angle
planet-to-star mass ratio q. In addition, the azimuthal of the secondary arm abruptly changes at large radii,
separationofthearmsisgenerallysmallerthan180◦ un- though interaction with a vortex may produce an un-
lessq becomesverylarge(q >0.01;Fung & Dong2015); expected outcome. In order to reproduce the lopsided
sothesecondaryisgenerallyaheadoftheprimaryatthe dust emission, a larger planetary mass of M = 15 M
p J
sameradius. Theobservedazimuthalseparationbetween is assumed so that the planet generates a stronger pres-
S1andS2(|φ −φ |)inSAO206462atR=0.3−0.′′35 sure bump at the gap edge. Also, because a more mas-
S1 S2
largely varies from 160◦ to 260◦,5, partly because of the sive planet opens a gap further away Rp = 120 au is
dip due to the depolarization effect around the minor- used: recall that the vortex forms at the inner gap edge
axis (see Garufi et al. 2013). Given the difficulties dis- whose position is a function of planetary mass. Since
criminating the primary and secondary, we test two sce- there is no boost via interaction between the spiral and
narios: (1) S1 being the primary and (2) S1 being the vortex as in the other scenario, significant vertical mo-
secondary. In both scenarios, we find that a vortex has tion inside the vortex will be required to explain the
to be locatedatthe southwesternside to explainthe ob- bright scattered light at the vortex position. In fact, it
served sub-millimeter dust emission peak. is possible thata vortexhasa three-dimensionalvertical
In Figure 4, we present the gas surface density distri- motion which can lift small particles to the disk atmo-
butionintheinner1”andthesimulatedALMAobserva- sphere, potentially enhancing the scattered light inten-
tion. The upper panels show the first scenario in which sity (Meheut et al. 2012).
S1 is assumedto be the primaryarm, with M =10 M It is possible that the spiral arms generate strong
p J
and R =100 au. Interestingly, the primary arm passes shocks and thus produce a high temperature near the
p
through the vortex at the inner gap edge. While re- surface (Zhu et al. 2015). Regarding the sub-millimeter
lating surface density to scattered light has to be done flux, however, high temperature near the surface would
with caution as pointed out earlier, it is plausible that not provide significant flux given that the disk is opti-
a spiral passing through a denser region would also pro- cally thin at 690 GHz as seen in Figure 5 and most of
duce higher density at the scattering surface. Also, be- the mass is concentrated near the midplane.
causetheprimaryarmgenerallyextendsfurtheroutand The vortex andthe inner spiralarms not only orbitat
has alargerpitchangle thanthe secondary,the lopsided differentfrequencyas pointedoutearlier,but they move
vortex-like structure can be naturally explained. The in a different manner. Figure 6 shows time evolution of
largeseparationbetween the secondaryand the primary the bright southwestern peak. If the peak is originated
from a spiral arm interacting with vortex it will appear
5SinceitisnotclearwhetherornotVispartofS1atthispoint, to be more opened over time, showing both circular and
wemeasuretheseparationbetweenS1andS2.
PLANETARY SIGNATURES IN SAO 206462 7
Fig.6.—Iso-densitycontours(Σg =20gcm−2)showingtimeevolutionofthebrightsouthwesternfeatureinthetwoscenarios: (left)S1
istheprimaryarmand(right)S1isthesecondaryarm. TheblackcontoursshowpositionsatthesametimeasinFigure4. Theblueand
red contours show positions at −10 and +10 years fromthe black contours, respectively. If the bright feature originates from the vortex
alone (scenario 2) it will move circularly over time, whereas the displacement will be circular + lateral if it is from a spiral arm passing
throughvortex(scenario1). Thecrosssymbolsindicatethepositionswherethedensitypeaksinthestructures.
lateral displacement. On the other hand, if the peak We have constructed two-dimensional models with
is due to the vortex alone, it will move only circularly. dust drift, which show vortex and spiral structure simi-
Assuming the vortex center is at 0.′′4=56 au, the peak lar to that observed in SAO 206462. We further suggest
will rotate about 1.◦1 per year. Since the two scenarios that an interaction between a spiral arm and the vortex
show noticeably different evolution, monitoring of the accounts for the abrupt change in brightness seen in the
brightest peak over the next few years will help reveal scattered light observations, although vortex alone may
the origin of the structures. also explain the bright scattered light peak. Monitoring
Pinilla et al. (2015) pointed out that the southwest- of the brightest peak over the next few years and higher
erndustemissionpeakisshiftedovertimebycomparing resolution ALMA observations can help test our models
two ALMA data sets obtained in 2012 and 2014. The andperhapssuggestwhichofourtwopreferredscenarios
shiftis,however,muchmoresignificantthanwhatwould is more likely.
be expected from our models. Instead, given that the
two ALMA data sets are taken at different frequencies
Theauthorsthanktheanonymousrefereeforahelpful
(690 and 340 GHz), it is possible that the observations
report that improved the initial manuscript. The au-
showoffsetsamongdustparticleswithdifferentsizesbe-
thors also thank Jeffrey Fung and Antonio Garufi for
cause particles with Stokes numbers closer to unity are
valuable discussion and Antonio Garufi et al. for mak-
known to show more violent movement inside a vortex
ing their data publicly available. Z.Z. greatly appreci-
(e.g. Bae et al. 2015).
ates Laurent Pueyo sharing his unpublished results and
We note that the observations so far were not able
providing very helpful suggestions. This research was
to reach the detection limit of ∼ 10 M at 100 au in
J supported in part by the University of Michigan, and
SAO 206462(e.g. Vicente et al.2011), because the ther-
computationalresourcesthereprovidedbyAdvancedRe-
mal emissions fromsuch planets are too smallcompared
search Computing. Z.Z. is supported by NASA through
to the central star. Future observations with GPI and
Hubble Fellowship grants HST-HF-51333.01-A awarded
SPHERE will be able to provide stronger constraints, if
by the Space Telescope Science Institute, which is op-
not detect a planet candidate.
erated by the Association of Universities for Research
Our calculations are limited to two dimensions and,
in Astronomy, Inc., for NASA, under contract NAS 5-
therefore, we are unable to conclude which scenario
26555. This paper makes use of the following ALMA
would be preferred over the other at this point. Fu-
data: ADS/JAO.ALMA #2011.0.00724.S. ALMA is a
turethree-dimensionalsimulationsandradiativetransfer
partnership of ESO (representing its member states),
calculations will be able to provide a more robust pre-
NSF (USA) and NINS (Japan), together with NRC
diction. In addition, knowing more accurate estimates
(Canada), NSC and ASIAA (Taiwan), and KASI (Re-
of the vortex position and disk temperature profile will
public of Korea), in cooperation with the Republic of
helpconstraintheplanetarymassandpositionforfuture
Chile. The Joint ALMA Observatory is operated by
searches.
ESO, AUI/NRAO and NAOJ. The National Radio As-
tronomy Observatory is a facility of the National Sci-
ence Foundation operated under cooperative agreement
5. CONCLUSIONS by Associated Universities, Inc.
8 Bae et al.
Fig. 7.—Distributionsof (left)gas, (middle)300 µmdust inφ−Rcoordinates, and (right)azimuthally averaged radialprofiles ofthe
gasanddustdistributionsatt=50.6Tp. ThesamemodelparametersareusedasinFigure1,butwithtwicehigherresolution(nR×nφ)
= (576×1376). In the rightpanel, the solidcurves show high-resolution (576×1376) results and the dashed curves show low-resolution
(288×688)results.
APPENDIX
RESOLUTION TEST
We double the resolutionin order to check numerical convergency,with a 10 M planet orbiting at 100 au. We test
J
with a particle size of a=300 µm as a representative case because (1) dust evolution does not affect to gas evolution
in our calculations and thus the gas structure remains identical no matter which dust particle size is used, and (2)
the dust stopping time often limits the time step in two-fluid calculations, especially when a small dust particle size
is assumed. For instance, when a = 30 µm is assumed, the dust stopping time is locally more than three orders of
magnitude shorter than the orbital time (see Figure 2), and therefore causes a very small time step.
InFigure7, wedisplaytwo-dimensionaldistributionsofgasand300µmdust,andtheir azimuthallyaveragedradial
profiles. While thehigh-resolutionrunshowsmoresmall-scalestructures,theoverallmorphologyisingoodagreement
with the low-resolution run presented in Figure 1. The azimuthally averaged radial density distributions are also
consistent with each other.
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